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Simplifying 9x2 + -60x + 80 = 0 Reorder the terms: 80 + -60x + 9x2 = 0 Solving 80 + -60x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 8.888888889 + -6.666666667x + x2 = 0 Move the constant term to the right: Add '-8.888888889' to each side of the equation. 8.888888889 + -6.666666667x + -8.888888889 + x2 = 0 + -8.888888889 Reorder the terms: 8.888888889 + -8.888888889 + -6.666666667x + x2 = 0 + -8.888888889 Combine like terms: 8.888888889 + -8.888888889 = 0.000000000 0.000000000 + -6.666666667x + x2 = 0 + -8.888888889 -6.666666667x + x2 = 0 + -8.888888889 Combine like terms: 0 + -8.888888889 = -8.888888889 -6.666666667x + x2 = -8.888888889 The x term is -6.666666667x. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667x + 11.11111112 + x2 = -8.888888889 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667x + x2 = -8.888888889 + 11.11111112 Combine like terms: -8.888888889 + 11.11111112 = 2.222222231 11.11111112 + -6.666666667x + x2 = 2.222222231 Factor a perfect square on the left side: (x + -3.333333334)(x + -3.333333334) = 2.222222231 Calculate the square root of the right side: 1.490711988 Break this problem into two subproblems by setting (x + -3.333333334) equal to 1.490711988 and -1.490711988.Subproblem 1
x + -3.333333334 = 1.490711988 Simplifying x + -3.333333334 = 1.490711988 Reorder the terms: -3.333333334 + x = 1.490711988 Solving -3.333333334 + x = 1.490711988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = 1.490711988 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = 1.490711988 + 3.333333334 x = 1.490711988 + 3.333333334 Combine like terms: 1.490711988 + 3.333333334 = 4.824045322 x = 4.824045322 Simplifying x = 4.824045322Subproblem 2
x + -3.333333334 = -1.490711988 Simplifying x + -3.333333334 = -1.490711988 Reorder the terms: -3.333333334 + x = -1.490711988 Solving -3.333333334 + x = -1.490711988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = -1.490711988 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = -1.490711988 + 3.333333334 x = -1.490711988 + 3.333333334 Combine like terms: -1.490711988 + 3.333333334 = 1.842621346 x = 1.842621346 Simplifying x = 1.842621346Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.824045322, 1.842621346}
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